2020/04/17 by Andrea Pelissetto, Davide Rossini, Ettore Vicari
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Condensed matter physics #Geometry #Hamiltonian (control theory) #Ising model #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Periodic boundary conditions #Phase (matter) #Phase boundary #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.102.012143
published as Phys. Rev. E 102, 012143 (2020) · 11 pages
arxiv created 2020/04/17 · openalex publication_date 2020/07/22 · arxiv updated 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We address the out-of-equilibrium dynamics of a many-body system when one of its Hamiltonian parameters is driven across a first-order quantum transition (FOQT). In particular, we consider systems subject to boundary conditions favoring one of the two phases separated by the FOQT. These issues are investigated within the paradigmatic one-dimensional quantum Ising model, at the FOQTs driven by the longitudinal magnetic field h, with boundary conditions that favor the same magnetized phase (EFBC) or opposite magnetized phases (OFBC). We study the dynamic behavior for an instantaneous quench and for a protocol in which h is slowly varied across the FOQT. We develop a dynamic finite-size scaling theory for both EFBC and OFBC, which displays some remarkable differences with respect to the case of neutral boundary conditions. The corresponding relevant timescale shows a qualitative different size dependence in the two cases: it increases exponentially with the size in the case of EFBC, and as a power of the size in the case of OFBC.